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Algebra, STD2 A1 2010 HSC 18 MC v1

Which of the following correctly express  \(h\)  as the subject of  \(A=\dfrac{bh}{2}\) ?

  1. \(h=\dfrac{A-2}{b}\)
  2. \(h=2A-b\)
  3. \(h=\dfrac{2A}{b}\)
  4. \(h=\dfrac{Ab}{2}\)
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\(C\)

Show Worked Solution
\(A\) \(=\dfrac{bh}{2}\)
\(bh\) \(=2A\)
\(\therefore\ h\) \(=\dfrac{2A}{b}\)

 
\(\Rightarrow C\)

Algebra, STD1 A1 2019 HSC 34

Given the formula  `C = (A(y + 1))/24`, calculate the value of  `y`  when  `C = 120`  and  `A = 500`.   (3 marks)

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`4.76`

Show Worked Solution

`text(Make)\ \ y\ \ text(the subject:)`

♦♦ Mean mark 32% (Std1).

`C` `= (A(y + 1))/24`
`24C` `= A(y + 1)`
`y + 1` `= (24C)/A`
`y` `= (24C)/A-1`
  `= (24 xx 120)/500-1`
  `= 4.76`

Algebra, STD2 A1 2019 HSC 11 MC

Which of the following correctly expresses `y` as the subject of the formula  `3x-4y-1 = 0`?

  1.  `y = 3/4 x-1`
  2.  `y = 3/4 x + 1`
  3.  `y = (3x-1)/4`
  4.  `y = (3x + 1)/4`
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`C`

Show Worked Solution

♦ Mean mark 50%.

`3x-4y-1` `= 0`
`4y` `= 3x-1`
`:. y` `= (3x-1)/4`

 
`=> C`

Algebra, STD2 A1 2016 HSC 24 MC

Which of the following correctly expresses `Q` as the subject of  `e = iR + Q/C`?

  1. `Q = Ce + CiR`
  2. `Q = Ce-CiR`
  3. `Q = (e + iR)/C`
  4. `Q = (e-iR)/C`
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`B`

Show Worked Solution
`e` `= iR + Q/C`
`Q/C` `= e-iR`
`:. Q` `= C(e-iR)= Ce-CiR`

 
`=> B`

Algebra, STD2 A1 2015 HSC 28d

The formula  `C = 5/9 (F-32)`  is used to convert temperatures between degrees Fahrenheit `(F)` and degrees Celsius `(C)`.

Convert 3°C to the equivalent temperature in Fahrenheit.   (2 marks)

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`37.4`

Show Worked Solution
`C` `= 5/9(F-32)`
`F-32` `= 9/5C`
`F`  `= 9/5C + 32`

 
`text(When)\ \ C = 3,`

`F= (9/5 xx 3) + 32= 37.4`

Algebra, STD2 A1 2007 HSC 19 MC

Which of the following correctly expresses  `T`  as the subject of  `B = 2pi (R + T/2)`?

  1. `T = B/pi-2R`
  2. `T = B/pi-R`
  3. `T = 2R-B/pi`
  4. `T = B/(4pi)-R/2`
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`A`

Show Worked Solution
`B` `= 2pi (R + T/2)`
`B/(2pi)` `= R + T/2`
`T/2` `= B/(2pi)-R`
`T` `= B/pi-2R`

 
`=>  A`

Algebra, STD2 A1 2010 HSC 18 MC

Which of the following correctly express  `x`  as the subject of  `a=(nx)/5` ?

  1. `x=(an)/5`
  2. `x=(5a)/n`
  3. `x=(a-5)/n`
  4. `x=5a-n`
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`B`

Show Worked Solution
`a` `=(nx)/5`
`nx` `=5a`
`x` `=(5a)/n`

 
`=>  B`

Algebra, STD2 A1 2013 HSC 21 MC

Which equation correctly shows  `r`  as the subject of  `S=800(1-r)`?

  1. `r=(800-S)/800`
  2. `r=(S-800)/800`
  3. `r=800-S`
  4. `r=S-800`
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`A`

Show Worked Solution
♦♦♦ Mean mark 27%
`S` `=800(1-r)`
`1-r` `=S/800`
`r` `=1-S/800`
  `=(800-S)/800`

 
`=>\ A`